PhD., University of Maryland
Jonathan is a published author and recently completed a book on physics and applied mathematics.
All lenses and mirrors can use ray diagrams to find images. There are three principal rays. The first principal ray occurs when the light comes in parallel to the principle axis, it goes out through the focus. The second principal ray occurs when light comes in through the focus, then it comes out parallel to the principle axis. The third principal ray occurs when the light goes straight through the vertex without changing its direction.
So let's talk about ray diagrams and Geometric optics now this is a really simple way for you to understand Geometrically where the image comes from basically from any lens or any mirror really simple and it works extremely well, if you do this on graph paper and you measure with a ruler it will come out exactly the way it's supposed to come out. Great alright so what we're going to do is we're going to use straight lines to find these images, we're going to draw 3 principal rays. And these 3 rays come from the standard properties of Geometric optics and of lenses. So if the light comes in parallel to the principle axis it goes out through the focus. If the light that's the first, second one if the light comes in through the focus then it goes out parallel so it's like doing this backwards. The last one says it goes straight through the vertex without changing it's direction at all. Alright so let's see how we use this, so I've got this situation down here, now I'm keeping in mind it's a converging lens I draw a focus on either side alright. So I've got a focal length which is the distance from the vertex here to this focus and that's the same length that's on the other side.
Alright first principal, in parallel out through focus easy enough, in parallel out through focus there it is. Alright second one in through focus out parallel, so now I'm going to use the fact that I've drawn a focus on the other side also. In through focus out parallel now notice that these guys are already crossing right there. So I've already located my image but the third one is just kind of to make sure that it all makes sense. So this is straight through the vertex and that one goes through there too. So that means that my image is right here notice that it is inverted, it's also real, it's real because all these light rays actually go through that point. Notice that the inversion makes perfect sense green was on top over here, he's on bottom over here alright so that's the way that it works. I locate my image nice and simple.
Okay so this is where the converging lens, where you're further away now remember if you get closer to the converging lens than the focus something weird happens. So let's see that something weird happen. Alright so over here I've got another converging lens and this time I'm closer to the lens than the focus. Alright let's see, in parallel out through focus well that's easy enough we got that one. Alright next one, in through focus out parallel, well the focus is kind of on the wrong side so what I have to interpret that to mean is that I want the ray that looks like it was coming from the focus out parallel. Notice that these two rays are never going to meet on the proper side of the lens, so that's going to indicate a virtual. Let's just check that out, well I've got straight through so there it is, notice that these guys really are not meeting.
Alright so now what I need to do to make them meet is I need to pretend that I'm this side of the lens I'm looking at that light and I want to know what does it look like it's coming from. Now where is it actually coming from? It's actually coming from the object, where does it look like it's coming from? Well this red line looks like it's coming from there this green line looks like it's coming from there and this blue line looks like and look at that. They all look like they're coming from this location right here, this is my image location notice that he is erect, he is virtual because the light didn't actually go through that point right and he's magnified he's much bigger. And of course that's why converging lenses are used as magnifying glasses. You take any magnifying glass you want to you feel on both sides and you'll feel that it is indeed convex glass on both sides. Convex so it's a converging lens.
Alright now let's see what happens with diverging lenses, these are a little weird I have to say but once you get the hung of it it's not too, too bad. Alright remember what the green one did in parallel out through focus alright in parallel. What does it mean out through focus I don't want to draw it down like that because that's not what diverging lenses do. So what we need to do is we need to write it as if it was coming from that focus. So the focus now was on this side, the focus that I'm thinking about so what I'm going to do is I'm going to draw a dashed line as if it's coming so see that's what I mean by out through focus. It doesn't actually go through the focus it just comes out in the direction that it would come from as if it was coming from the focus.
Alright let's do blue, blue says in through focus out parallel. Alright in through focus, well which focus? Not this one, it's got to come in through this focus. So it's going to come in as if it was going to this focus. So what I'm going to do is I'm going to draw a straight line that would continue to that focus. So once it hits the lens instead of doing that it's going to go out parallel alright. Alright great so there's two of them, the last one is always the easiest straight through vertex okay I can do that and I'm done right and so now I'm looking on this side of the lens and I want to see where does it look like the light is coming from. Well this red is fine, the blue looks like it's coming from here, the green looks like it's coming from that focus and so therefore I'm all done I got my image he is right here alright.
He is erect or upright and he is a virtual image that is magnification less than 1 it's smaller than the object. And that's the way that it goes, these diverging lenses are the most complicated ones but they're really not that bad once you get the hung of them. What I would suggest you do, is sit down with a piece of graph paper and you can make up these examples just as easily as I can. You draw 2 perpendicular lines and you draw an x on one side and then you make sure that you draw an x on the other side that's the same distance away. If you're doing it right, your light ways will always converge to one point. And that's ray diagrams.